Asymptotic Geometry of Teichmuller Space: Thickness and Divergence

Harold Sultan (Columbia)

Abstract: I will talk about the asymptotic geometry of Teichmuller space equipped with the Weil-Petersson metric. In particular, I will give a criterion for determining when two points in the asymptotic cone of Teichmuller space can be separated by a point; motivated by a similar characterization in mapping class groups by Behrstock-Kleiner-Minsky-Mosher and in right angled Artin groups by Behrstock-Charney. I will also explain two new ways to uniquely characterize the Teichmuller space of the genus two once punctured surface amongst all Teichmuller spaces: one is that it is thick of order two and the other is that it has a divergence function which is superquadratic yet subexponential.